In Track 4, go through the waterfall and stop at the series of tight turns. There is a road on the left that doubles back. Follow it to find a plateau with a sword in a stone.
Track 3 shortcut
About half way around the course there is a barrier guiding your car to the left. Ignore it and drive through the wall into an underground passage.
Track 4 shortcut
Approximately a quarter of the way around the track is a waterfall, off which you can jump. This waterfall has a rock on top of it. Line yourself up just to the right of the rock, and aim slightly towards the right. You will jump just to the right of the opposite waterfall into a storm drain.
Track 7 shortcut
There is an old train track at the beginning of the race. Race along this fast enough and jump from section to section, and cut off part of the track.